Adaptive-optics-based turbulence mitigation in a 400 Gbit/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices: publisher's note.

This publisher's note contains a correction to Opt. Lett.48, 6452 (2023)10.1364/OL.506270.

Adaptive-optics-based turbulence mitigation in a 400†Git/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices.

In general, atmospheric turbulence can degrade the performance of free-space optical (FSO) communication systems by coupling light from one spatial mode to other modes. In this Letter, we experimentally demonstrate a 400 Gbit/s quadrature-phase-shift-keyed (QPSK) FSO mode-division-multiplexing (MDM) coherent communication link through emulated turbulence using four Laguerre Gaussian (LG) modes with different radial and azimuthal indices (L G 10, L G 11, L G -10, and L G -11). To mitigate turbulence-induced channel cross talk and power loss, we implement an adaptive optics (AO) system at the receiver end. A Gaussian beam at a slightly different wavelength is co-propagated with the data beams as the probe beam. We use a wavefront sensor (WFS) to measure the wavefront distortion of this probe beam, and this information is used to tune a spatial light modulator (SLM) to adaptively correct the four distorted data-beam wavefronts. Using this adaptive-optics approach, the power loss and cross talk are reduced by ∼10 and ∼18 dB, respectively.

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation.

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Atmospheric turbulence strength distribution along a propagation path probed by longitudinally structured optical beams.

Atmospheric turbulence can cause critical problems in many applications. To effectively avoid or mitigate turbulence, knowledge of turbulence strength at various distances could be of immense value. Due to light-matter interaction, optical beams can probe longitudinal turbulence changes. Unfortunately, previous approaches tended to be limited to relatively short distances or large transceivers. Here, we explore turbulence probing utilizing multiple sequentially transmitted longitudinally structured beams. Each beam is composed of Bessel-Gaussian ([Formula: see text]) modes with different [Formula: see text] values such that a distance-varying beam width is produced, which results in a distance- and turbulence-dependent modal coupling to [Formula: see text] orders. Our simulation shows that this approach has relatively uniform and low errors (<0.3 dB) over a 10-km path with up to 30-dB turbulence-structure-constant variation. We experimentally demonstrate this approach for two emulated turbulence regions (~15-dB variation) with <0.8-dB errors. Compared to previous techniques, our approach can potentially probe longer distances or require smaller transceivers.

Automatic turbulence mitigation for coherent free-space optical links using crystal-based phase conjugation and fiber-coupled data modulation.

There are various performance advantages when using temporal phase-based data encoding and coherent detection with a local oscillator (LO) in free-space optical (FSO) links. However, atmospheric turbulence can cause power coupling from the Gaussian mode of the data beam to higher-order modes, resulting in significantly degraded mixing efficiency between the data beam and a Gaussian LO. Photorefractive crystal-based self-pumped phase conjugation has been previously demonstrated to "automatically" mitigate turbulence with limited-rate free-space-coupled data modulation (e.g., <1 Mbit/s). Here, we demonstrate automatic turbulence mitigation in a 2-Gbit/s quadrature-phase-shift-keying (QPSK) coherent FSO link using degenerate four-wave-mixing (DFWM)-based phase conjugation and fiber-coupled data modulation. Specifically, we counter-propagate a Gaussian probe from the receiver (Rx) to the transmitter (Tx) through turbulence. At the Tx, we generate a Gaussian beam carrying QPSK data by a fiber-coupled phase modulator. Subsequently, we create a phase conjugate data beam through a photorefractive crystal-based DFWM involving the Gaussian data beam, the turbulence-distorted probe, and a spatially filtered Gaussian copy of the probe beam. Finally, the phase conjugate beam is transmitted back to the Rx for turbulence mitigation. Compared to a coherent FSO link without mitigation, our approach shows up to ∼14-dB higher LO-data mixing efficiency and achieves error vector magnitude (EVM) performance of <16% under various turbulence realizations.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

High-capacity free-space optical communications using wavelength- and mode-division-multiplexing in the mid-infrared region.

Due to its absorption properties in atmosphere, the mid-infrared (mid-IR) region has gained interest for its potential to provide high data capacity in free-space optical (FSO) communications. Here, we experimentally demonstrate wavelength-division-multiplexing (WDM) and mode-division-multiplexing (MDM) in a ~0.5 m mid-IR FSO link. We multiplex three ~3.4 µm wavelengths (3.396 µm, 3.397 µm, and 3.398 µm) on a single polarization, with each wavelength carrying two orbital-angular-momentum (OAM) beams. As each beam carries 50-Gbit/s quadrature-phase-shift-keying data, a total capacity of 300 Gbit/s is achieved. The WDM channels are generated and detected in the near-IR (C-band). They are converted to mid-IR and converted back to C-band through the difference frequency generation nonlinear processes. We estimate that the system penalties at a bit error rate near the forward error correction threshold include the following: (i) the wavelength conversions induce ~2 dB optical signal-to-noise ratio (OSNR) penalty, (ii) WDM induces ~1 dB OSNR penalty, and (iii) MDM induces ~0.5 dB OSNR penalty. These results show the potential of using multiplexing to achieve a ~30X increase in data capacity for a mid-IR FSO link.

Utilizing multiplexing of structured THz beams carrying orbital-angular-momentum for high-capacity communications.

Structured electromagnetic (EM) waves have been explored in various frequency regimes to enhance the capacity of communication systems by multiplexing multiple co-propagating beams with mutually orthogonal spatial modal structures (i.e., mode-division multiplexing). Such structured EM waves include beams carrying orbital angular momentum (OAM). An area of increased recent interest is the use of terahertz (THz) beams for free-space communications, which tends to have: (a) larger bandwidth and lower beam divergence than millimeter-waves, and (b) lower interaction with matter conditions than optical waves. Here, we explore the multiplexing of THz OAM beams for high-capacity communications. Specifically, we experimentally demonstrate communication systems with two multiplexed THz OAM beams at a carrier frequency of 0.3 THz. We achieve a 60-Gbit/s quadrature-phase-shift-keying (QPSK) and a 24-Gbit/s 16 quadrature amplitude modulation (16-QAM) data transmission with bit-error rates below 3.8 × 10-3. In addition, to show the compatibility of different multiplexing approaches (e.g., polarization-, frequency-, and mode-division multiplexing), we demonstrate an 80-Gbit/s QPSK THz communication link by multiplexing 8 data channels at 2 polarizations, 2 frequencies, and 2 OAM modes.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.

Receiver aperture and multipath effects on power loss and modal crosstalk in a THz wireless link using orbital-angular-momentum multiplexing.

The channel capacity of terahertz (THz) wireless communications can be increased by multiplexing multiple orthogonal data-carrying orbital-angular-momentum (OAM) beams. In THz links using OAM multiplexing (e.g., Laguerre-Gaussian [Formula: see text] beams with p = 0), the system performance might degrade due to limited receiver aperture size and multipath effects. A limited-size aperture can truncate the received beam profile along the radial direction. In addition, due to beam divergence, part of the beam might interact with reflectors in the environment, causing the signal to reflect and interfere at the receiver with the directly propagating part of the beam; this is known as the multipath effect. In this paper, we simulate and analyze the impact of both effects on the equality of the THz OAM link by considering a full two-dimensional (2-D) LG modal set. The simulation results show (i) a limited-size receiver aperture can induce power loss and modal power coupling mainly to LG modes with the same ℓ but p > 0 for directly propagated OAM beams; (ii) the multipath effect can induce modal power coupling across multiple 2-D LG modes, which leads to inter-channel coupling among the different channels in an OAM multiplexed link; (iii) the interference between the reflected and direct beams can induce intra-channel coupling between the received signals from the reflected and direct beams; and (iv) beams with a higher OAM order (e.g., from ± 1 to ± 5) or a lower carrier frequency (e.g., from 0.1 to 1 THz) experience larger intra- and inter-channel coupling. The intra- and inter-channel coupling in an OAM-multiplexed THz link can degrade the signal-to-noise ratio (SNR) and induce SNR penalty when compared to a single-channel system.

Demonstration of turbulence mitigation in a 200-Gbit/s orbital-angular-momentum multiplexed free-space optical link using simple power measurements for determining the modal crosstalk matrix.

We experimentally demonstrate turbulence mitigation in a 200-Gbit/s quadrature phase-shift keying (QPSK) orbital-angular-momentum (OAM) mode-multiplexed system using simple power measurements for determining the modal coupling matrix. To probe and mitigate turbulence, we perform the following: (i) sequentially transmit multiple probe beams at 1550-nm wavelength each with a different combination of Laguerre-Gaussian (LG) modes; (ii) detect the power coupling of each probe beam to LG0,0 for determining the complex modal coupling matrix; (iii) calculate the conjugate phase of turbulence-induced spatial phase distortion; (iv) apply this conjugate phase to a spatial light modulator (SLM) at the receiver to mitigate the turbulence distortion for the 1552-nm mode-multiplexed data-carrying beams. The probe wavelength is close enough to the data wavelength such that it experiences similar turbulence, but is far enough away such that the probe beams do not affect the data beams and can all operate simultaneously. Our experimental results show that with our turbulence mitigation approach the following occur: (a) the inter-channel crosstalk is reduced by ∼25 and ∼21 dB for OAM +1 and -2 channels, respectively; (b) the optical signal-to-noise ratio (OSNR) penalty is <1 dB for both OAM channels for a bit error rate (BER) at the 7% forward error correction (FEC) limit, compared with the no turbulence case.

Turbulence-resilient pilot-assisted self-coherent free-space optical communications using a photodetector array for bandwidth enhancement.

We experimentally demonstrate a 4-Gbit/s 16-QAM pilot-assisted, self-coherent, and turbulence-resilient free-space optical link using a photodetector (PD) array. The turbulence resilience is enabled by the efficient optoelectronic mixing of the data and pilot beams in a free-space-coupled receiver, which can automatically compensate for turbulence-induced modal coupling to recover the data's amplitude and phase. For this approach, a sufficient PD area might be needed to collect the beams while the bandwidth of a single larger PD could be limited. In this work, we use an array of smaller PDs instead of a single larger PD to overcome the beam collection and bandwidth response trade-off. In the PD-array-based receiver, the data and pilot beams are efficiently mixed in the aggregated PD area formed by four PDs, and the four mixing outputs are electrically combined for data recovery. The results show that: (i) either with or without turbulence effects (D/r0 = ∼8.4), the 1-Gbaud 16-QAM signal recovered by the PD array has a lower error vector magnitude than that of a single larger PD; (ii) for 100 turbulence realizations, the pilot-assisted PD-array receiver recovers 1-Gbaud 16-QAM data with a bit-error rate below 7% of the forward error correction limit; and (iii) for 1000 turbulence realizations, the average electrical mixing power loss of a single smaller PD, a single larger PD, and a PD array is ∼5.5 dB, ∼1.2 dB, and ∼1.6 dB, respectively.

Auxiliary controller design and performance comparative analysis in closed-loop brain-machine interface system.

Brain-machine interface (BMI) can realize information interaction between the brain and external devices, and yet the control accuracy is limited by the change of electroencephalogram signals. The introduction of auxiliary controller can overcome the above problems, but the performance of different auxiliary controllers is quite different. Hence, in this paper, we comprehensively compare and analyze the performance of different auxiliary controllers to provide a theoretical basis for designing BMI system. The main work includes: (1) designing four kinds of auxiliary controllers based on simultaneous perturbation stochastic approximation-function approximator (SPSA-FA), iterative feedback tuning-PID (IFT-PID), model predictive control (MPC) and model-free control (MFC); (2) based on the model of improved single-joint information transmission, constructing the closed-loop BMI systems with the decoder-based Wiener filter; and (3) comparing their performance in the constructed closed-loop BMI systems for dynamic motion restoration. The results show that the order of tracking accuracy is MPC, IFT-PID, SPSA-FA, MFC, and the order of time consumed is opposite. A good control effectiveness is achieved at the expense of time, so a suitable auxiliary controller should be selected according to the actual requirements.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters.

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l0 at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l0 with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l0; and (3) the OAM components of the generated beam could be tuned either by changing the value of l0, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Demonstration of generating a 100 Gbit/s orbital-angular-momentum beam with a tunable mode order over a range of wavelengths using an integrated broadband pixel-array structure.

We experimentally generate an orbital-angular-momentum (OAM) beam with a tunable mode order over a range of wavelengths utilizing an integrated broadband pixel-array OAM emitter. The emitter is composed of a 3-to-4 coupler, four phase controllers, and a mode convertor. An optical input is split into four waveguides by the coupler. Subsequently, the four waveguide fields are coherently combined and transformed into a free-space OAM beam by the mode convertor. By tuning the phase delay Δφ between the four waveguides using the integrated phase controllers, the OAM order of the generated beam could be changed. Our results show that (a) a single OAM beam with a tunable OAM order (ℓ=-1 or ℓ=+1) is generated with the intermodal power coupling of <-11dB, and (b) in a wavelength range of 6.4 nm, a free-space link of a single 50 Gbaud quadrature-phase-shift-keying (QPSK) channel carried by the tunable OAM beam is achieved with a bit error rate below the forward-error-correction threshold. As proof of concept, a 400 Gbit/s OAM-multiplexed and WDM QPSK link is demonstrated with a ∼1-dB OSNR penalty compared with a single-beam link.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode.

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge (ℓ) but different kr (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

Tunable Doppler shift using a time-varying epsilon-near-zero thin film near 1550 nm.

We experimentally investigate the tunable Doppler shift in an 80 nm thick indium-tin-oxide (ITO) film at its epsilon-near-zero (ENZ) region. Under strong and pulsed excitation, ITO exhibits a time-varying change in the refractive index. A maximum frequency redshift of 1.8 THz is observed in the reflected light when the pump light has a peak intensity of ∼140GW/cm2 and a pulse duration of ∼580fs, at an incident angle of 40°. The frequency shift increases with the increase in pump intensity and saturates at the intensity of ∼140GW/cm2. When the pump pulse duration increases from ∼580fs to ∼1380fs, the maximum attainable frequency shift decreases from 1.8 THz to 0.7 THz. In addition, the pump energy required to saturate the frequency shift decreases with the increase in pump pulse duration for ∼x<1ps and remains unchanged for ∼x>1ps durations. Tunability exists among the pump pulse energy, duration, and incident angle for the Doppler shift of the ITO-ENZ material, which can be employed to design efficient frequency shifters for telecom applications.

Adiabatic Frequency Conversion Using a Time-Varying Epsilon-Near-Zero Metasurface.

A time-dependent change in the refractive index of a material leads to a change in the frequency of an optical beam passing through that medium. Here, we experimentally demonstrate that this effect-known as adiabatic frequency conversion (AFC)-can be significantly enhanced by a nonlinear epsilon-near-zero-based (ENZ-based) plasmonic metasurface. Specifically, by using a 63-nm-thick metasurface, we demonstrate a large, tunable, and broadband frequency shift of up to ∼11.2 THz with a pump intensity of 4 GW/cm2. Our results represent a decrease of ∼10 times in device thickness and 120 times in pump peak intensity compared with the cases of bare, thicker ENZ materials for the similar amount of frequency shift. Our findings might potentially provide insights for designing efficient time-varying metasurfaces for the manipulation of ultrafast pulses.

Modal coupling and crosstalk due to turbulence and divergence on free space THz links using multiple orbital angular momentum beams.

Orbital-angular-momentum (OAM) multiplexing has been utilized to increase the channel capacity in both millimeter-wave and optical domains. Terahertz (THz) wireless communication is attracting increasing attention due to its broadband spectral resources. Thus, it might be valuable to explore the system performance of THz OAM links to further increase the channel capacity. In this paper, we study through simulations the fundamental system-degrading effects when using multiple OAM beams in THz communications links under atmospheric turbulence. We simulate and analyze the effects of divergence, turbulence, limited-size aperture, and misalignment on the signal power and crosstalk of THz OAM links. We find through simulations that the system-degrading effects are different in two scenarios with atmosphere turbulence: (a) when we consider the same strength of phasefront distortion, faster divergence (i.e., lower frequency; smaller beam waist) leads to higher power leakage from the transmitted mode to neighbouring modes; and (b) however, when we consider the same atmospheric turbulence, the divergence effect tends to affect the power leakage much less, and the power leakage increases as the frequency, beam waist, or OAM order increases. Simulation results show that: (i) the crosstalk to the neighbouring mode remains < - 15 dB for a 1-km link under calm weather, when we transmit OAM + 4 at 0.5 THz with a beam waist of 1 m; (ii) for the 3-OAM-multiplexed THz links, the signal-to-interference ratio (SIR) increases by ~ 5-7 dB if the mode spacing increases by 1, and SIR decreases with the multiplexed mode number; and (iii) limited aperture size and misalignment lead to power leakage to other modes under calm weather, while it tends to be unobtrusive under bad weather.

Experimental mitigation of the effects of the limited size aperture or misalignment by singular-value-decomposition-based beam orthogonalization in a free-space optical link using Laguerre-Gaussian modes.

Limited-size receiver (Rx) apertures and transmitter-Rx (Tx-Rx) misalignments could induce power loss and modal crosstalk in a mode-multiplexed free-space link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s four-data-channel free-space optical link. To mitigate the above degradations, our approach of singular-value-decomposition-based (SVD-based) beam orthogonalization includes (1) measuring the transmission matrix H for the link given a limited-size aperture or misalignment; (2) performing SVD on the transmission matrix to find the U, Σ, and V complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre-Gaussian modes with complex weights according to the V matrix; and (4) applying the U matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multi-mode beams show that (a) with a limited-size aperture, the power loss and crosstalk could be reduced by ∼8 and ∼23dB, respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by ∼15 and ∼40dB, respectively.